Misallocation and Financial Market Frictions:

Some Direct Evidence from the Dispersion in Borrowing Costs

Simon Gilchrist∗ Jae W. Sim† Egon Zakrajsek‡

October 29, 2012

Abstract

Financial frictions distort the allocation of resources among productive units—all else equal,firms whose financing choices are affected by such frictions face higher borrowing costs than firmswith ready access to capital markets. As a result, input choices may differ systematically acrossfirms in ways that are unrelated to their productive efficiency. We propose an accounting frame-work that allows us to assess empirically the magnitude of the loss in aggregate resources due tosuch misallocation. To a second-order approximation, the framework requires only informationon the dispersion in borrowing costs across firms, which we measure—for a subset of U.S. man-ufacturing firms—directly from the interest rate spreads on their outstanding publicly-tradeddebt. Given the observed dispersion in borrowing costs, our approximation method implies arelatively modest loss in efficiency due to resource misallocation—on the order of 1 to 2 percentof measured total factor productivity (TFP). In our framework, the correlation between firmsize and borrowing costs has no bearing on TFP losses under the assumption that financialdistortions and firm-level efficiency are jointly log-normally distributed. To take into accountthe effect of covariation between firm size and borrowing costs, we consider a more generalframework, which dispenses with the assumption of log-normality and which implies somewhathigher estimates of the resource losses—about 3.5 percent of measured TFP. Counterfactualexperiments indicate that dispersion in borrowing costs must be an order of magnitude higherthan that observed in the U.S. financial data, in order for misallocation—arising from financialdistortion—to account for a significant fraction of measured TFP differentials across countries.

JEL Classification: D92, O16, O40Keywords: total factor productivity, financial distortions, firms-specific borrowing costs

We thank participants at the RED Mini-Conference on “Misallocation and Productivity” (which took place at the2011 SED Annual Meetings) for helpful comments. We are also grateful to Benjamin Moll, Diego Restuccia (the GuestEditor), Richard Rogerson, and two anonymous referees for numerous insightful comments and suggestions. SamuelHaltenhof and Ben Rump provided excellent research assistance. All errors and omissions are our own responsibilityalone. The views expressed in this paper are solely the responsibility of the authors and should not be interpreted asreflecting the views of the Board of Governors of the Federal Reserve System or of anyone else associated with theFederal Reserve System.

∗Department of Economics Boston University and NBER. E-mail: sgilchri@bu.edu†Division of Research & Statistics, Federal Reserve Board. E-mail: jae.w.sim@frb.gov‡Division of Monetary Affairs, Federal Reserve Board. E-mail: egon.zakrajsek@frb.gov

1 Introduction

Economists have long emphasized that distortions in the allocation of resources across heteroge-

neous firms can have large adverse effects on aggregate productivity and on the gains from trade

(cf. Hopenhayn and Rogerson [1993], Guner, Ventura, and Xu [2008], and Hopenyahn [2011]). Sim-

ilarly, Restuccia and Rogerson [2008] have argued that systematic and persistent differences in the

allocation of resources across production units of varying productivity may be an important deter-

minant of differences in income per capita across countries, a hypothesis that seems to be borne

out by the data. For example, using detailed microdata on manufacturing establishments in China

and India, Hsieh and Klenow [2009] estimate that resource misallocation accounts for 30 to 60 per-

cent of the difference between the total factor productivity (TFP) in U.S. manufacturing and the

corresponding sectoral TFP in China and India.1

In light of the enormous differences in the depth and sophistication of financial mar-

kets between developed and developing countries, a large literature has long stressed the

role of finance in economic development; see Matsuyama [2007] for a comprehensive review.

More recently, Amaral and Quintin [2010], Greenwood, Sanchez, and Wang [2010, 2012], and

Buera, Kaboski, and Shin [2011] have developed theoretical models, which show—in a quantitative

sense—that a large portion of cross-country differences in TFP may attributable to resource mis-

allocation arising from imperfect financial markets. In a recent paper, however, Midrigan and Xu

[2010] challenge these findings, arguing that financial distortions can account for only a modest

portion (on the order of 5 percent) of the difference in manufacturing TFP between Columbia and

South Korea, the latter being a benchmark country with highly developed capital markets. Thus,

the extent to which financial frictions lead to reductions in TFP through resource misallocation

appears to be an open question.

Although the TFP accounting methodology developed by Hsieh and Klenow [2009] leads to a

persuasive conclusion that large differences in manufacturing TFP between advanced and develop-

ing economies reflect the dispersion in marginal revenue products across heterogeneous plants, it also

suggests that there are substantial measured TFP losses in U.S. manufacturing. At the same time,

Hsieh and Klenow [2009] are careful to ascribe such losses to potential measurement error rather

than to the underlying frictions hampering the process of allocation of resources across firms. This

tension raises an important question regarding the extent to which measures of dispersion based

on plant-level marginal revenue products paint an accurate picture of resource misallocation that

can be attributed directly to financial frictions, as opposed to alternative sources of frictions such

as policy-induced tax distortions, gaps between average and marginal products due to adjustment

costs, fixed production costs, or other measurement-related issues.

In this paper, we address this tension by developing an alternative TFP accounting procedure,

1As shown by Klenow and Rodrıguez-Clare [1997] and Hall and Jones [1999] differences in income per capita acrosscountries are primarily accounted for by low TFP in poorer countries.

1

which relies on direct measures of firms’ borrowing costs to measure the implied resource misallo-

cation caused by distortions in credit markets. Specifically, we develop an accounting framework in

which observed differences in borrowing costs across firms can be mapped into measures of aggre-

gate resource misallocation that may plausibly be attributed to financial market frictions. Using a

log-normal approximation, we show that the extent of resource misallocation can be inferred from

cross-industry or cross-country information on the dispersion in borrowing costs.

We apply our accounting framework to a panel of U.S. manufacturing firms drawn from the

Compustat database. Despite fairly large and persistent differences in borrowing costs across firms,

our estimates imply relatively modest losses in TFP due to resource misallocation—roughly on the

order of 3.5 percent of TFP in the U.S. manufacturing sector. This finding is consistent with the

recent work of Hopenyahn [2011], whose quantitative analysis also suggests modest TFP losses for

economically plausible degrees of micro-level distortions.

Our results can be obtained directly from the log-normal approximation and information on the

dispersion of interest rates across firms. Nonetheless, our methodology also allows us to relax the

log-normal approximation and infer TFP losses using the joint distribution of sales and borrowing

costs. We find that the estimated losses under this approach closely match those obtained under

the assumption of log-normality. This finding demonstrates both the robustness of our results

and its applicability to a broader environment where firm-level data on the joint distribution of

sales and borrowing costs may not be readily available. We also compare the measured dispersion

in the observed user cost of capital to the dispersion in the user cost inferred from the realized

revenue products, an approach consistent with the methodology of Hsieh and Klenow [2009]. We

find that using the latter approach, the dispersion in the implied user cost overstates the degree of

dispersion—and hence the degree of resource misallocation—by a factor of four, compared with an

approach that uses data on actual borrowing costs.

In the wake of the recent financial crisis, research into business cycle fluctuations such as that

of Gilchrist, Sim, and Zakrajsek [2011], Khan and Thomas [2011], and Arellano, Bai, and Kehoe

[2012] has analyzed the importance of dispersion in productivity for resource misallocation in en-

vironments where firms face imperfect financial markets. Contributing to this vein of research, we

document a significant increase in the overall dispersion in firms’ borrowing costs over the past

decade. Although our results indicate that the overall loss in measured TFP due to the dispersion

in borrowing costs is relatively small, this secular increase in the dispersion of borrowing costs

implies a reduction in the aggregate TFP growth on the order of 20 to 40 basis points per year over

the 2000–10 period. This finding suggests that increased heterogeneity in access to external finance

may indeed have important macroeconomic consequences even in countries with well-developed

financial markets such as the United States.

The road map for the remainder of the paper is as follows. In the next section, we present

some basic facts regarding the dispersion in observed borrowing costs for our sample of U.S. man-

2

ufacturing firms. In Section 3, we develop our accounting framework. Section 4 presents our main

empirical results along with several robustness exercises. Section 5 concludes.

2 Borrowing Costs and Firm Size: Some Some Stylized Facts

In this section, we briefly describe our unique data set on firm-level borrowing costs and present

some stylized facts about the relationship between the cross-sectional dispersion in borrowing costs

and firm size.

2.1 Data Description

Our main analysis focuses on a subset of U.S. manufacturing corporations. The distinguishing

characteristic of these firms is that they have access to the corporate bond market. For a panel

of such firms covered by the Standard & Poor’s (S&P) Compustat and the Center for Research

in Security Prices (CRSP), we obtained month-end secondary market prices of their outstanding

securities from the Lehman/Warga and Merrill Lynch databases.2 By limiting the sample to senior

unsecured issues with a fixed coupon schedule, we ensure that external borrowing costs of different

firms are measured at the same point in their capital structure.

Using the secondary market prices of individual securities, we construct the corresponding

credit spreads—measured relative to risk-free Treasury rates—based on the methodology described

in Gilchrist and Zakrajsek [2012]. To ensure that our results are not driven by a small number of

extreme observations, we eliminated all observations with credit spreads below 5 basis points and

greater than 1,000 basis points, cutoffs corresponding roughly to the 2.5th and 97.5th percentiles of

the credit spread distribution, respectively. In addition, we eliminated from our sample very small

corporate issues (par value of less than $1 million) and all observations with a remaining term-to-

maturity of less than one year or more than 30 years. These selection criteria yielded a sample

of 2,623 individual securities over the 1985:M1–2010:M12 period. We matched these corporate

securities with their issuer’s quarterly income and balance sheet data from Compustat and daily

data on equity valuations from CRSP, a procedure that yielded a matched sample of 496 firms,

split about equally between durable and nondurable goods manufacturing industries.

Table 1 contains summary statistics for the key characteristics of bonds in our sample. Note

that a typical firm in our sample has only a few senior unsecured issues outstanding at any point

in time—the median firm, for example, has two such issues trading in any given month. This

distribution, however, exhibits a significant positive skew, as some firms can have many more issues

trading in the secondary market at a point in time. To calculate a firm-specific credit spread in

any given month, we simply average the spreads on the firm’s outstanding bonds in that month.3

2These two proprietary data sources include secondary market prices for a vast majority of dollar-denominatedbonds publicly issued in the U.S. corporate cash market; see Gilchrist, Yankov, and Zakrajsek [2009] for details.

3As a robustness check, we also computed firm-specific spreads as a weighted average of credit spreads on the

3

Table 1: Selected Corporate Bond Characteristics

Variable Mean SD Min P50 Max

No. of bonds per firm/month 2.86 3.04 1.00 2.00 52.0Mkt. value of issue ($mil.)a 358.9 360.1 1.22 260.4 5,628Maturity at issue (yrs.) 12.8 9.2 1.0 10.0 40.0Term to maturity (yrs.) 10.8 8.5 1.0 7.7 30.0Duration (years) 6.42 3.36 0.92 5.92 15.8Credit rating (S&P) - - D A3 AAACoupon rate (pct.) 7.06 1.97 1.70 6.85 15.25Nominal effective yield (pct.) 6.80 2.20 0.46 6.71 19.89Credit spread (bps.) 170 157 5 116 1,000

Note: Sample period: 1985:M1–2010:M12; Obs. = 141,770; No. of bonds = 2,623; No. of firms = 496.Sample statistics are based on trimmed data (see text for details).a Market value of the outstanding issue deflated by the CPI (2005 = 100).

The distribution of the market values of these issues is similarly skewed, with the range running

from $1.2 million to more than $5.6 billion. The maturity of these debt instruments is fairly long,

with the average maturity at issue of almost 13 years; the average remaining term-to-maturity

in our sample is 10.84 years. In terms of default risk—at least as measured by the S&P credit

ratings—our sample spans the entire spectrum of credit quality, from “single D” to “triple A.” At

“A3,” however, the median observation is still solidly in the investment-grade category. An average

bond has an expected return of 170 basis points above the comparable risk-free rate, while the

standard deviation of 157 basis points reflects the wide range of credit quality in our sample.

We focus on the 1985–2010 period because it is characterized by a growing tendency for U.S.

corporate borrowing to take the form of negotiable securities issued directly in capital markets.

The resulting deepening of the corporate bond market has led to a substantial degree of disinter-

mediation, as well as to the development of well-functioning markets in derivatives, in which credit,

interest rate, and currency risks, for example, can be readily hedged.

A full-fledged corporate bond market tends to be also associated with sound financial reporting

systems, a thriving community of professional financial analysts, multiple credit rating agencies,

a wide range of corporate debt instruments demanding sophisticated credit analysis, and efficient

procedures for corporate reorganization and liquidation, factors that greatly facilitate the process

of price discovery for corporate debt claims.4 Indeed, a well-developed corporate bond market

is in a much better position than the banking system—which is heavily leveraged and subject

to regulatory imperfections—to exert a crucial disciplinary role exercised by market forces.5 As

firm’s outstanding bonds, with weights equal to the market value of each issue. This alternative weighting procedurehad no effect on any of the results reported in the paper.

4For example, using high-frequency bond transaction prices of U.S. firms, Hotchkiss and Ronen [2002] find thatthe informational efficiency of corporate bond prices is similar to that of the underlying stocks.

5As shown by the theoretical work of Hakansson [1982], the financial system with a well-developed bond marketwill—under fairly general conditions—Pareto-dominate a financial system in which banks do most of the lending.

4

Figure 1: Growth of Real Sales in U.S. Manufacturing

1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009-30

-25

-20

-15

-10

-5

0

5

10

15Percent

Firms with access to the corporate bond marketAll publicly-traded firms

Quarterly

Note: Sample period: 1985:Q1–2010:Q4. The solid line depicts the quarterly growth rate of real sales forour sample of 496 manufacturing firms that have access to the corporate bond market; the dotted line depictsthe growth rate of real sales for all publicly-traded U.S. manufacturing firms in Compustat. The nominalsales are deflated by the implicit price deflator for the nonfarm business sector output (2005 = 100); all dataare seasonally adjusted. The shaded vertical bars represent the NBER-dated recessions.

a result, the variation in our firm-specific interest rates likely reflects the dispersion in “true”

borrowing costs both across firms and over time.6

Although our sample is restricted to manufacturing firms with the access to the corporate

bond market, these 496 firms account, on average, for about 50 percent of total sales in U.S.

manufacturing over the 1985–2010 period. Moreover, as shown in Figure 1, the cyclical fluctuations

in their sales closely match the growth of sales of all publicly-traded manufacturing firms in the

Compustat database. In combination with the fact that our sample of firms spans a wide range

of credit quality (see Table 1), these features of the data suggest that the dispersion in borrowing

costs for this subset of firms is likely representative of the manufacturing sector as a whole.

6In fact, Gilchrist and Zakrajsek [2007] use such firm-specific interest rates to construct the user cost of capitalfor a large panel of U.S. nonfinancial firms. According to their results, investment spending is highly responsive tofluctuations in the user cost of capital that utilizes firm-specific interest rates; moreover, their estimates of the long-runelasticity of capital with respect to the user costs are very close to unity, a result consistent with the Cobb-Douglasproduction technology.

5

Figure 2: Distribution of Firm-Level Borrowing Costs

0.0

0.1

0.2

0.3

0.4

0.5

0.6Density

0 100 200 300 400 500 600 700 800 900Credit spread (basis points)

Note: The histogram depicts the distribution of firm-specific average credit spreads for our sample of496 manufacturing firms.

2.2 Firm-Level Borrowing Costs and Firm Size

To get a sense of the cross-sectional dispersion in firm-level borrowing costs, we calculate the average

credit spread for each firm over time, a measure of debt financing costs that abstracts from the

substantial cyclical variation that characterizes credit spreads at business cycle frequencies. The

resulting distribution is shown in Figure 2. The central tendency of the distribution—as measured

by its mean—is 240 basis points, while its standard deviation is about 160 basis points. Recall

that this specific sample trims the upper tail of the distribution of credit spreads at 1,000 basis

points, so the standard deviation of 160 basis points likely underestimates the true dispersion of

credit spreads in the U.S. manufacturing sector.

To the extent that distortions in credit markets arising from agency conflicts between borrowers

and lenders—as evidenced by the persistent dispersion in credit spreads—influence the firms’ op-

timal input choices, we expect to see a negative relationship between firm size and credit spreads.

In Figure 3, we plot the average credit spread for each firm over time against the average firm size

as measured by real sales; the solid line shows the fitted values from regressing the firm-specific

average credit spread on a second-order polynomial function of the logarithm of real sales. The fact

6

Figure 3: Firm-Level Borrowing Costs and Firm Size

0

100

200

300

400

500

600

700

800

900

1000

Real sales ($millions, logarithmic scale)

50 250 1000 5000 25000

Cre

dit s

prea

d (b

asis

poi

nts)

Note: The scatter plot depicts the relationship between firm-specific average credit spreads and average firmsize, as measured by real sales, for our sample of 496 manufacturing firms. The nominal sales are deflatedby the implicit price deflator for the nonfarm business sector output (2005 = 100).

that we are averaging over time implies that this relationship is capturing the long-term relation-

ship between firm size and borrowing costs in the U.S. manufacturing sector. The strong negative

relationship evident in the data is consistent with the notion that access to finance is an important

determinant of the allocation of resources across firms.

As is well known, however, credit spreads capture both the likelihood of default and a residual

component that relates to firm-specific factors such as loss given default and pricing terms reflecting

individual firm characteristics.7 The likelihood of default is intimately related to leverage of the

firm. Thus, to the extent that smaller firms are more leveraged, they will be considered by investors

as being of lower credit quality and thus face higher spreads in the debt markets.

To control for differences in default risk across firms, we estimate the following regression:

sit = β1DDit + β2DD2it + λt + ǫit,

7In the corporate finance literature, there is a well-known result—the “credit spread puzzle”—which shows thatless than one-half of the variation in corporate bond credit spreads can be attributed to the financial health of theissuer (e.g., Elton, Gruber, Agrawal, and Mann [2001]). As shown by Collin-Dufresne, Goldstein, and Martin [2001],Houwelling, Mentink, and Vorst [2005], Driessen [2005], and Duffie, Saita, and Wang [2007], the unexplained portionof the variation in credit spreads appears to reflect some combination of time-varying liquidity premium, to someextent the tax treatment of corporate bonds, and a default-risk factor.

7

Figure 4: Residual Credit Spreads and Firm Size

-300

-200

-100

0

100

200

300

400

500

Real sales ($millions, logarithmic scale)

50 250 1000 5000 25000

Res

idua

l cre

dit s

prea

d (b

asis

poi

nts)

Note: The scatter plot depicts the relationship between firm-specific average residual credit spreads andaverage firm size, as measured by real sales, for our sample of 496 manufacturing firms. The nominal salesare deflated by the implicit price deflator for the nonfarm business sector output (2005 = 100).

where sit denotes the credit spread of firm i in month t, DDit is the distance-to-default for firm i,

and λt is the time fixed effect that controls for common cyclical shocks. The key feature of the

above specification is that the firm-specific (time-varying) default risk is captured by the distance-

to-default (DD), a market-based indicator of credit risk based on the contingent claims framework

developed in the seminal work of Merton [1974]. Briefly, this option-theoretic approach assumes that

a firm has just issued a single zero-coupon bond of face value F that matures at date T . Rational

stockholders will default at date T only if the total value of the firm VT < F ; by assumption, the

rights of the bondholders are activated only at the maturity date, as stockholders will maintain

control of the firm even if the value of the firm Vs < F for some s < T . Under the assumptions

of the model, the probability of default—that is, Pr[VT < F ]—depends on the distance-to-default,

a volatility-adjusted measure of leverage inferred from equity valuations and the firm’s observed

capital structure.8

The regression fits the data quite well, explaining 55 percent of the variation in firm-specific

credit spreads. In Figure 4, we plot the firm-specific average residual credit spread (i.e., 1Ti

∑Ti

t=1 ǫit)

8In addition to being used widely by the financial industry, our choice of the Merton DD-framework is alsomotivated by the work of Schaefer and Strebulaev [2008], who present compelling micro-level evidence showing thatthe DD-model accounts well for the default-risk component of corporate bond prices. To calculate the DDs for oursample of firms, we employ a robust procedure developed by Bharath and Shumway [2008].

8

against the average firm size. Although the dispersion in credit spreads is reduced noticeably

once default risk is taken into account, we nevertheless still find a strong negative relationship

between the non-default component of credit spreads and firm size. Such permanent differences in

borrowing costs across firms imply that financial distortions play a potentially important role in

the misallocation of resources across firms.

3 The TFP Accounting Framework

In this section, we present the accounting framework that relates losses in TFP due to resource

misallocation to dispersion in firm-specific borrowing costs. Our procedure is derived from the

decreasing returns to scale production framework outlined in Midrigan and Xu [2010]; it is also

directly related to the TFP accounting procedure emphasized by Hsieh and Klenow [2009].

3.1 The Production Environment

We assume that firms (indexed by i) employing capital (K) and labor (L) have access to a decreasing

returns to scale production function of the form:

Yi = A1−ηi

(

K1−αi Lα

i

)η,

where 0 < η < 1 is the degree of decreasing returns in production and Ai is a firm-specific level of

productivity.9 Decreasing returns may be due to the managerial span of control as in Lucas [1978]

or, alternatively, due to monopolistic competition in an environment with Dixit-Stiglitz preferences

over heterogeneous goods.

We further assume that firms must borrow at a firm-specific interest rate ri in order to obtain

both capital and labor inputs. Letting 0 < δ < 1 denote the rate of capital depreciation and W

the aggregate wage, the optimal choice of inputs implies that firms equate the marginal revenue

products of capital and labor to their respective costs:

(1− α)ηYiKi

= ri + δ;

αηYiLi

= (1 + ri)W,

where the second equation captures the fact that we assume that labor costs reflect borrowing costs

as well as the aggregate wage.

9We interpret output as value added and assume that materials inputs enter the gross output production functionin a Leontief form; furthermore, we assume that firms do not face financing costs for materials inputs. We explorealternative production structures below.

9

In this framework, the optimal capital-labor ratio is given by

Ki

Li=

1− α

α

[

(1 + ri)W

ri + δ

]

.

Solving for the labor input yields

[(1 + ri)W ]

αηLi = A1−η

i

[

1− α

α

(

(1 + ri)W

ri + δ

)

Li

](1−α)η

Lαηi ,

which implies the optimal input choices:

Li = cLAi

[

(1 + ri)−

1−(1−α)η1−η (ri + δ)

−(1−α)η1−η

]

;

Ki = cKAi

[

(1 + ri)−

αη

1−η (ri + δ)−

1−αη

1−η

]

,

for some positive constants cL and cK .

Letting

wli ≡

[

(1 + ri)−

1−(1−α)η1−η (ri + δ)

−(1−α)η1−η

]

; (1)

wki ≡

[

(1 + ri)−

αη

1−η (ri + δ)−

1−αη

1−η

]

, (2)

then optimal input choices are proportional to firm-level productivity adjusted for firm-specific

differences in factor input costs:

Li = cLAiwli;

Ki = cKAiwki .

In this context, wli and wk

i denote labor and capital “wedges,” respectively, which induce distortions

in input choices relative to an efficient allocation of inputs. The efficient allocation of inputs across

firms is determined by setting wli = wl and wk

i = wk for all i.

3.2 Aggregation and TFP

Define aggregate labor and capital inputs according to

L = cL

∫

Aiwlidi and K = cK

∫

Aiwki di,

and define the wedge in the cost index as

wi = (wli)α(wk

i )1−α.

10

The aggregate output may then be expressed as

Y =

∫

Yidi = cαηL c(1−α)ηK

∫

Aiwηi di.

Total factor productivity is measured as aggregate output relative to a geometrically-weighted

average of aggregate labor and capital inputs:

TFP =Y

LαηK(1−α)η=

∫

Aiwηi di

(∫

Aiwlidi)

αη(∫

Aiwki di)

(1−α)η,

or in logs,

log(TFP ) = log

(∫

Aiwηi di

)

− αη log

(∫

Aiwlidi

)

− (1− α)η

(∫

Aiwki di

)

. (3)

Assuming that Ai, wli, and wk

i are jointly distributed according to a log-normal distribution,

logAi

logwli

logwki

∼ MVN

a

wl

wk

,

σ2a σa,wl

σa,wk

σa,wlσ2wl

σwl,wk

σa,wkσ2wl,wk

σ2wk

,

then the second-order approximations of the three terms in equation (3) are given by

log

(∫

Aiwηi di

)

= a+ η [αwl + (1− α)wk] +σ2a

2+

η2α2

2σ2wl

+η2(1− α)2

2σ2wk

+ η2α(1− α)σwl,wk+ η [ασwl,a + (1− α)σwk,a] ;

log

(∫

Aiwlidi

)

= a+ wl +σ2a

2+

σ2wl

2+ σwl,a;

log

(∫

Aiwki di

)

= a+ wk +σ2a

2+

σ2wk

2+ σwk,a.

Combining the above expressions and rearranging yields the second-order approximation of equa-

tion (3)

log(TFP ) = (1− η)

[

a+σ2a

2

]

−

ηα(1− ηα)

2σ2wl

−

η(1− α)[1− η(1− α)]

2σ2wk

+ η2α(1− α)Corr(wl, wk)σwlσwk

.

(4)

At this point, it is instructive to consider productivity gains that would arise from an efficient

allocation of resources in an economy with heterogeneous production units. Specifically, consider

a problem faced by a social planner, whose objective is to maximize aggregate output, subject to

the constraint that aggregate labor and capital are equal to the amounts used in the economy with

11

dispersion in input costs. Formally, this problem is given by

YE = maxKi,Li

∫

A1−ηi

(

K1−αi Lα

i

)ηdi,

subject to∫

Lidi = L and

∫

Kidi = K.

Letting λL and λK denote the Lagrange multipliers on the aggregate input constraints, then optimal

input choices imply constant factor input ratios across firms:

(1− α)ηYiKi

= λK and αηYiLi

= λL.

It is then straightforward to show that under this efficient allocation

YE =

(∫

Aidi

)(1−η)

K(1−α)ηLαη,

and the corresponding measure of TFP is given by

TFPE =YE

K(1−α)ηLαη=

(∫

Aidi

)(1−η)

.

In an economy with an efficient allocation of resources across heterogeneous production units, wki

and wli are constant (i.e., wl

i = wl and wki = wk for all i). In those circumstances, the second-order

approximation in equation (4) reduces to

log(TFPE) = (1− η)

[

a+σ2a

2

]

.

As the production environment in such an economy approaches constant returns-to-scale—that is,

η → 1—the aggregate TFP is equal to E[Ai], which is normalized to unity. With 0 < η < 1, the

above expression captures gains in economic efficiency arising solely from the benefits of dispersion

in firm size in the diminishing returns-to-scale production environment.

The relative TFP loss that is solely attributable to resource misallocation caused by the disper-

sion in input costs is given by

log

(

TFPE

TFP

)

=ηα(1− ηα)

2σ2wl

+η(1− α)[1− η(1− α)]

2σ2wk

− η2α(1− α)Corr(wl, wk)σwlσwk

.

(5)

Because aggregate inputs are held constant across the two allocations, the relative TFP loss is

exactly equivalent to the relative loss in aggregate output due to the inefficient allocation of inputs

12

implied by the presence of dispersion in input costs across firms.

Several comments about equation (5) are in order. First, this measure of TFP loss is an

increasing function of the dispersion in the labor and capital wedges σwland σwk

, respectively.

Second, up to a second-order (log-normal) approximation, the covariance between firm-level TFP

and the capital and labor wedges is irrelevant for the size—in percent terms—of the TFP loss due

to misallocation.10 And lastly, holding dispersion in the labor and capital wedges fixed, a high

correlation between the labor and capital wedges reduces the relative TFP loss due to resource

misallocation.

To gain some intuition for this last point, it is helpful to express aggregate output and inputs

as functions of the scale distortion wi and the distortion in the input mix zi ≡Ki

Li=

wki

wli

. That is,

Y =

∫

(Aiwi)ηdi, K =

∫

Aiwizαi di, and L =

∫

Aiwiz(α−1)i di.

We can then attribute the relative TFP loss to distortions in scale—as measured by σ2w—and

distortions in the input mix, as measured by σ2z :

log

(

TFPE

TFP

)

=η(1− η)

2σ2w +

ηα(1− α)

2σ2z ,

where

σ2w = α2σ2

wl+ (1− α)2σ2

wk+ 2α(1− α)Corr(wl, wk)σwl

σwk;

σ2z = σ2

wl+ σ2

wk− 2Corr(wl, wk)σwl

σwk.

In our framework, therefore, a high correlation between wk and wl is associated with increased scale

distortion but less variation in the input mix across firms. On net, the efficiency gain from reduced

variation in the input mix outweighs the efficiency loss owing to increased variation in firm size by

the amount η2α(1− α)Corr(wl, wk)σwlσwk

.

3.3 Resource Misallocation and the Dispersion in Interest Rates

To derive an approximate relationship between the dispersion in interest rates and TFP losses

due to the misallocation of resources, we first consider a case in which both the labor and capital

input choices are fully distorted by financial market frictions (i.e., capital input costs are ri+ δ and

labor input costs are given by (1 + ri)W ). In that case, Corr(wl, wk) = 1, and the log-labor and

10Note that up to a second-order approximation, this implies that in percent terms, size-based distortions matterto the extent that they create dispersion in the labor and capital wedges and not because they are based on sizeper se. Thus, distortions brought about by frictions in credit markets, government policies, and other institutionalfactors that influence the size-distribution of firms, or that disproportionately distort the input mix across the sizedistribution, have a negative effect on TFP, precisely because they induce variation in the input wedges.

13

log-capital wedges are given by

logwli = −

1− (1− α)η

1− ηlog (1 + ri)−

(1− α)η

1− ηlog (ri + δ) ;

logwki = −

αη

1− ηlog (1 + ri)−

1− αη

1− ηlog (ri + δ) .

The first-order approximations of the log wedges around log(ri) are then given by

logwli ≈ −

1

1− η

[

(1− (1− α)η)r

1 + r+ (1− α)η

r

r + δ

]

log(ri);

logwki ≈ −

1

1− η

[

αηr

1 + r+ (1− αη)

r

r + δ

]

log(ri).

Thus, the ratio of the standard deviation of the labor wedge relative to the capital wedge can be

approximated asσwl

σwk

≈

[(1− (1− α)η)(r + δ) + (1− α)η(1 + r)]

[αη(r + δ) + (1− αη) (1 + r)].

We can then approximate the relative TFP loss as

log

(

TFPE

TFP

)

=

[

η(1− α) [1− η(1− α)]

2+

ηα(1− αη)

2

(

σwl

σwk

)2

− η2α(1− α)σwl

σwk

]

σ2wk

, (6)

where

σwk=

1

1− η

[

αηr

1 + r+ (1− αη)

r

r + δ

]

σlog(r).

The first term in equation (6) reflects the direct effect of variation in wk on the resource misalloca-

tion. The second term captures the direct effect of variation in wl, while the third term is due to

the covariance between wl and wk.

Now, consider the case where financial market frictions induce firm-level variation in the user-

cost of capital (ri + δ) but do not cause firm-level variation in labor input costs (1 + r)W . In

this case, the labor wedge wl varies across firms solely because of the induced variation in the

capital-labor ratio. As a result,σwl

σwk

≈

(1− α)η

1− αη,

and the relative TFP loss can be expressed as

log

(

TFPE

TFP

)

=

[

η(1− α) [1− η(1− α)]

2−

ηα(1− αη)

2

(

σwl

σwk

)2]

σ2wk

, (7)

where

σwk=

[

(1− αη)

1− η

] [

r

r + δ

]

σlog(r).

14

Eliminating financial distortions in the labor market reduces the variability of the capital and labor

wedges (i.e., σwkand σwk

) and, for chosen parameter values, leaves the ratioσwl

σwk

about unchanged.

The negative sign in front of the second term in equation equation (7) reflects the fact that, on

net, the labor-input distortion, as evidenced by σwl> 0, lowers the overall TFP loss by reducing

the variation in the input mix across firms.11 As we show below, eliminating financial distortions

in the labor market reduces TFP losses relative to the case where firms face borrowing constraints

in both labor and capital markets.

4 Results

In this section, we use our framework to provide some estimates of TFP losses for the U.S. man-

ufacturing sector implied by resource misallocation arising from financial market frictions. Specif-

ically, we use the information on the dispersion of firm-specific borrowing costs to calculate the

implied TFP loss, an approach that relies on the assumption of log-normality when computing the

second-order approximation of the relative TFP loss. By utilizing the corresponding information

on firm-level sales, we show that this approximation provides a reasonable estimate of TFP losses

due to resource misallocation.

In our analysis, we assume that the firm-specific borrowing costs in quarter t—denoted by rit—

are equal to the real risk-free long-term interest rate r∗t , augmented by the firm-specific premium

given by the credit spread sit:12

rit = r∗t + sit.

For the real risk-free rate r∗t , we use the difference between the 10-year nominal Treasury yield and

the average expected CPI inflation over the next 10 years, as measured by the Philadelphia Fed’s

Survey of Professional Forecasters. In all exercises, we set the depreciation rate δ = 0.06, the labor

share α = 2/3, and the degree of decreasing returns to scale η = 0.85, values that are standard in

the literature.

Figure 5 depicts the time-series evolution of the cross-sectional distribution of real interest

rates for our sample of manufacturing firms with access to the corporate bond market. The shaded

band around the median real interest rate (the solid line) depicts the 90th (P90) and 10th (P10)

percentiles of the distribution of borrowing costs at each point in time. Over the 1985–2010 period,

the P90–P10 range has fluctuated in the range between 140 basis and 670 basis points, an indication

of a significant time-series variation in the dispersion of firm-level borrowing costs.

According to our accounting framework, we can infer logwlit and logwk

it for each firm in our

sample using equations (1) and (2) and the firm-specific real interest rate rit. Given these wedges,

11While this result is algebraically true for the case of no direct financial distortions in labor markets, numericalcomputations show that it also holds in the more general case.

12Quarterly credit spread sit is calculated as a simple average of the corresponding monthly credit spreads.

15

Figure 5: Dispersion of Firm-Level Borrowing Costs in U.S. Manufacturing

1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 0

2

4

6

8

10

12Percent

Quarterly

1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 0

2

4

6

8

10

12Percent

MedianP90-P10

Quarterly

Note: Sample period: 1985:Q1–2010:Q4. The solid line depicts the median of real interest rates for oursample of 496 manufacturing firms that have access to the corporate bond market; the shaded band depictsthe corresponding P90–P10 range. The shaded vertical bars represent the NBER-dated recessions.

we can compute their respective standard deviations σwland σwk

. Using equation (5), we can then

calculate the implied TFP loss due to resource misallocation arising from financial market frictions.

The above procedure relies only on the dispersion in real interest rates to compute TFP losses

due resource misallocation. Given data on firm-level (real) sales—denoted by Yit—and firm-specific

interest rates, it is possible to infer directly the implied capital and labor inputs, according to

Lit =αηYit

(1 + rit)Wand Kit =

(1− α)ηYitrit + δ

.

Summing over sales and the implied inputs yields

Y =1

NT

∑

i

∑

t

Yit, K =1

NT

∑

i

∑

t

Kit, and L =1

NT

∑

i

∑

t

Lit,

which allows us to calculate the implied aggregate TFP:

TFP =Y

(L)αη(K)(1−α)η.

16

To infer the level of aggregate TFP that would prevail in the case of the efficient allocation of

resources, we first need to compute the firm-specific level of TFP using the relationship

Ait =Yitwit

,

where wit = (wlit)

αη(wkit)

(1−α)η is the geometrically-weighted average of the labor and capital

wedges. The efficient level of inputs (KE

it , LE

it), along with the efficient level of output Y E

it , can

be obtained using the relationships:

KE

it = cKAitwk, LE

it = cLAitwl, and Y E

it = Ait/w,

where wk and wl are the average capital and labor wedges observed in the data and w = (wl)α(wk)1−α.

Letting

Y E =1

NT

∑

i

∑

t

Y E

it , KE =1

NT

∑

i

∑

t

KE

it , and LE =1

NT

∑

i

∑

t

LE

it

denote the aggregate output, capital, and labor that would be obtained under the efficient allocation

of resources, the corresponding implied aggregate TFP—the level of TFP that would prevail in the

absence of dispersion in borrowing costs—is given by

TFPE =Y E

(LE)αη(KE)(1−α)η,

and the relative TFP loss due to resource misallocation by

Relative TFP Loss = log

(

TFPE

TFP

)

.

Importantly, by using data on firm-specific sales and borrowing costs, we can infer the relative

TFP loss due to resource misallocation without relying on the log-normal approximation. On the

other hand, to the extent that there are significant nonfinancial distortions that influence firm size,

the accounting procedure that relies on both borrowing costs and sales may, in fact, overstate the

true loss in TFP that may be attributable to financial distortions. Thus, we view the log-normal

approximation as a lower bound and the size-based measure as an upper bound to the potential

TFP losses that may be attributed to resource misallocation brought about by frictions in credit

markets.

The results of these two exercises are summarized in Table 2. We calculate the implied TFP

losses for all 496 firms in our sample as well as for durable- and nondurable-goods producers

separately. The entries under the heading “Approximate” are the implied TFP losses (in percent)

calculated using only the dispersion in the firm-specific borrowing costs and rely on the log-normal

17

Table 2: TFP Losses due to Resource Misallocation(Manufacturing Firms with Access to the Corporate Bond Market)

Relative TFP Loss

Sector r σr [rP10, rP90] σwlσwk

Approximate Actual

All Manufacturing 2.43 1.66 [0.84, 4.71] 0.43 0.59 1.75 3.44(1.40) -

Durable Goods Mfg. 2.62 1.69 [0.92, 4.99] 0.43 0.60 1.77 3.23(1.42) -

Nondurable Goods Mfg. 2.24 1.61 [0.73, 4.67] 0.42 0.58 1.69 3.63(1.36) -

Note: Sample period: 1985:Q1–2010:Q4; No. of firms = 496; Obs. = 16,975. Real interest rates and theimplied TFP losses are in percent. The approximate TFP losses use only the information on the dispersion offirm-specific average real interest rates and rely on the second-order log-normal approximation; the approximateTFP losses reported in parentheses are calculated under the assumption that financial market frictions distortonly the choice of the capital input. The actual TFP losses employ information on the firm-specific real interestrates and the corresponding real sales (see text for details).

approximation; the entries under the heading “Actual” are the implied TFP losses that employ

information on both borrowing costs and sales. Columns labeled r, σr, and [rP10, rP90] contain the

sample mean, the standard deviation, and the P90–P10 range, respectively, of the average firm-

specific borrowing costs, while σwland σwk

denote the estimates of the cross-sectional standard

deviation of the log labor and capital wedges used to compute the approximate TFP losses.

The results in Table 2 indicate that the loss in U.S. manufacturing TFP due to resource mis-

allocation arising from financial market frictions is relatively modest. The losses implied by our

approximation method are about 1.7 percent for the manufacturing sector as a whole and for its

two main subsectors. As discussed in Section 3.3, the TFP loss in the model where financial fric-

tions distort labor and capital input costs exceeds the loss in the model where financing frictions

influence only the user cost of capital. In this latter case, the implied TFP loss for U.S. manufac-

turing, reported in parentheses, is 1.4 percent. Thus, financial frictions in both labor and capital

markets imply only a modest increase in TFP losses relative to the model in which such frictions

only influence the cost of capital inputs.

The actual TFP losses—that is, losses computed using the information on firm-specific bor-

rowing costs and the corresponding sales—are around 3.5 percent for the manufacturing sector as

a whole; as before, the estimated losses are highly comparable across the two subsectors. From

an economic perspective, however, both methods imply TFP losses that are sufficiently close in

magnitude, which suggests that the log-normal approximation provides a reasonable estimate of

the TFP losses in the case where only information on the dispersion of borrowing costs across firms

is available.

With these results in hand, we now consider the implications of two counterfactual scenarios,

both of which assume greater dispersion in borrowing costs than actually observed in the U.S. data.

18

Table 3: Counterfactual TFP Losses due to Resource Misallocation

Scenario r σr [rP10, rP90] σwlσwk

Loss

S1: rit = r∗t + 2sit 4.84 3.30 [1.68, 9.41] 0.68 0.93 4.31(3.26)

S2: rit = r∗t + 10sit 24.2 16.5 [8.38, 46.7] 1.57 1.95 19.9(11.0)

Note: Real interest rates and the implied TFP losses are in percent. The approximate TFPlosses use only the information on the dispersion of firm-specific average real interest rates andrely on the second-order log-normal approximation; the approximate TFP losses reported inparentheses are calculated under the assumption that financial market frictions distort onlythe choice of the capital input.

In the first scenario, we assume that

rit = r∗t + 2sit,

which roughly doubles the dispersion in firm-level real interest rates; the second scenario counter-

factually assumes that

rit = r∗t + 10sit,

which represents a ten-fold increase in the dispersion of borrowing costs.

As reported in the S1 row of Table 3, doubling the dispersion in firm-specific credit spreads

implies an approximate loss in manufacturing TFP of 4.3 percent, assuming that financial market

frictions distort the firm’s choice of both the capital and labor inputs; assuming that financing

constraints apply only to the capital input implies a TFP loss of about 3.3 percent. According to

the S2 row, a ten-fold increase in the dispersion of firm-level borrowing costs implies a significant

loss in TFP as a result of resource misallocation. Under this counterfactual scenario, the implied

loss in TFP, according to our log-normal approximation, is almost 20 percent in the case in which

borrowing constraints apply to both the labor market and the market for physical capital.

Note, however, that the ten-fold increase in credit spreads that underlies this counterfactual

scenario implies an average real interest rate of almost 25 percent, with the P90–P10 range of

8.38 percent to 46.7 percent, an extremely high and disperse distribution of borrowing costs com-

pared with the actual U.S. data. Indeed, one suspects that the first two moments of this counter-

factual distribution are high even relative to the mean and dispersion in borrowing costs that one

is likely to observe in developing economies, other than the very poor ones.13

13Measuring borrowing costs in developing economies, especially for countries that are in early stages of develop-ment, is complicated by the fact that a significant portion of credit to businesses and households is extended throughinformal sources (i.e., relatives, small shopkeepers, and money lenders). Nevertheless, the available evidence indicatesthat in the poorest countries, in addition to a very high average level of borrowing costs, there is a considerable degreeof dispersion in interest rates across borrowers; see Banerjee and Duflo [2005, 2010] and references therein for details.

19

4.1 Gross vs. Value-Added Output and the Role of Material Inputs

The accounting framework described above applies to value-added output and ignores the role of

material inputs in the production process, which in the manufacturing sector account for about

one-half of gross output. A common assumption in the production function literature (e.g., Basu

[1996]) is that material inputs and value-added output enter the gross output production function

in Leontief form:

Yi = min

{

Yiθy

,Mi

θm

}

,

where Yi denotes gross output, Yi is value-added output, and Mi is the quantity of materials input,

while θy and θm capture the gross shares of value added output and materials in production,

respectively. In this case, the profit function is given by

Πi = min

{

Yiθy

,Mi

θm

}

− (ri + δ)Ki − (1 + ri)WLi − (1 + rmi )PmMi,

where Pm denotes the price of the materials input and rmi is the corresponding financing cost.

Given the Leontief production structure, optimality requires that Mi = θmθy

Yi. The optimal

choices of capital and labor are now modified to include the cost of material inputs in the production

process:

(1− α)ηYiKi

=ri + δ

1θy

−

[

θmPm

θy

]

(1 + rmi );

αηYiLi

=(1 + ri)W

1θy

−

[

θmPm

θy

]

(1 + rmi ).

First, consider a situation in which the financing cost of the materials input is zero—that is,

rmi = 0. In that case, the presence of the materials input in the production process only rescales

costs associated with capital and labor inputs and does not affect the dispersion of the two revenue

products. Hence, it has no implications for the measured TFP loss. Furthermore, gross output is

proportional to its value-added counterpart, and our TFP accounting procedure is valid for either

measure of output.

Alternatively, suppose rmi = ri, so that the financing cost of the materials input is the same

as that of capital and labor inputs. In this case, we need to modify the wedges to account for

the additional financing costs. Specifically, the presence of the materials input in the production

process will increase the dispersion of the wedges for a given dispersion in ri. With Pm = 1, the

share of materials in gross output of one-half implies that θy = θm = 0.5. Then, the cost of capital

is(

ri+δ1−ri

)

and the cost of labor is(

1+ri1−ri

)

W . Following the procedure outlined above, and ignoring

terms involving r2, the first-order approximations of the log-wedges around log(ri) are now given

20

Table 4: TFP Losses due to Resource Misallocation(Alternative Production Structures)

Capital Share (1− α) (1) (2)

1− α = 1/6 0.73 1.261− α = 1/3 1.76 2.551− α = 1/2 3.16 4.19

Note: The implied TFP losses are in percent and are computedusing the second-order log-normal approximation. Column 1 re-ports TFP losses under the assumption that financial frictionsdistort both the labor and capital inputs but not the materialsinput. Column 2 reports TFP losses assuming that the materialsinput is combined with value added output in a Leontief produc-tion function to determine gross output.

by

logwli ≈ −

1

1− η

[

2(1− (1− α)η)r + αη

(

r + δr

r + δ − δr

)]

log(ri);

logwki ≈ −

1

1− η

[

2αηr + (1− αη)

(

r + δr)

r + δ − δr

)]

log(ri).

Because δr is close to zero, the need to finance the materials input has a negligible effect on the

dispersion of wedges through its effect on the cost of capital. By contrast, it does roughly double

the dispersion of the labor wedge by increasing the dispersion in the cost of labor input.

As an alternative to the Leontief production technology, suppose that the materials input is

substitutable with both labor and capital. Assuming a Cobb-Douglas production function, let Li

denote a composite labor-materials input bundle that must be financed at the cost of (1 + ri)W .

We may then interpret Yi as gross output and modify the capital share to reflect a gross-output

production function. If the materials input share of gross output is 1/2 and the capital share of

value added is 1/3, this implies that the capital share of gross output is 1/6. Thus to allow for

the materials input in a Cobb-Douglas production technology, it is sufficient to use the accounting

procedure outlined in Section 2 but lower the capital share appropriately.

Table 4 reports the effect of allowing the materials input to enter the gross-output production

function in Leontief form and the effect of varying the capital share on the second-order approx-

imation to the loss function. Column 1 reports the TFP loss associated with the baseline model,

a case in which the labor and capital input choices are distorted by financial frictions. Column 2

reports the TFP loss in the case where financial frictions also distort the choice of the materials

input. For each of these alternative production structures, we consider capital shares of 1/6, 1/3,

and 1/2.

Assuming that gross output is a Leontief function of value-added output and the materials

input, the implied TFP losses increase—relative to the baseline case in which financial frictions

apply only to the capital and labor inputs—when we allow for financial frictions to influence the

21

choice of the materials input. The increase in the TFP loss, however, is modest. In particular,

when 1− α = 1/3, a case that is most relevant in that comparison, the relative TFP loss increases

from 1.76 percent to 2.55 percent.

To understand the effect of substitutability of inputs on the TFP losses, one should compare

the baseline model (Column 1) with 1−α = 1/6 to the model with the materials input (Column 2)

with 1 − α = 1/3. The baseline model with 1 − α = 1/6 can be interpreted as a production

structure where gross output depends on capital, labor, and materials within a Cobb-Douglas

production function. The model with the materials input and 1 − α = 1/3, in contrast, can be

interpreted as a production structure where value-added output is a Cobb-Douglas function of labor

and capital, and the materials input enters the gross output production function in the Leontief

form. Switching from unit elasticity to no substitutability for the materials input increases the

TFP loss from 0.73 percent to 2.55 percent. It is important to remember that the cost of capital is

more sensitive to variation in interest rates than the cost of labor and material inputs. Reducing

the substitutability between capital and other inputs magnifies the importance of financial friction

on capital input choices and increases the overall TFP loss. Nonetheless, these effects appear to be

relatively modest even if one completely eliminates any form of substitutability between value-added

output and the materials input.

Overall, these results imply that our finding that dispersion in borrowing costs across firms

results in relatively modest TFP losses is robust to alternative assumptions regarding the production

structure and the various input financing choices. In general, TFP losses are highest in situations

where the capital share is high, substitutability among inputs is low, and financial frictions apply

to all inputs.

4.2 Comparison with Hsieh–Klenow Methodology

As noted in the introduction, the methodology proposed by Hsieh and Klenow [2009] implies sizable

TFP losses for the U.S. manufacturing sector due to misallocation. Their methodology relies on

measured dispersion in marginal revenue products of labor and capital, though they recognize that

plant-based marginal revenue products may contain substantial measurement error; indeed, they

argue against interpreting the implied TFP losses for the U.S. manufacturing sector as evidence

for resource misallocation. Although our data set contains manufacturing firms rather than plants

and does not include labor input choices, we can nonetheless gauge the implications of applying

their methodology to our data set by comparing the dispersion in the marginal revenue product

of capital—as measured by the sales-to-capital ratio—to the dispersion in the cost of capital as

measured by firm-specific interest rates. More specifically, the implied dispersion in the cost of

capital can be inferred directly from the measured dispersion in the log of the sales-to-capital ratio.

Table 5 reports the dispersion in the log of the sales-to-capital ratio and the log of the cost

of capital as measured by log(rit + δ). The first row reports the overall standard deviation, while

22

Table 5: Comparison of Dispersion Measures

Std. Deviation

Dispersion Measure log(rit + δ) log(Sit/Ki,t−1) Ratioa

Overall 0.149 0.690 4.629Industry adjusted 0.144 0.565 3.911Long-run/industry adjusted 0.126 0.574 4.540

Note: Sample period: 1985:Q1–2010:Q4; No. of firms = 496; Obs. = 16,975. Overall standarddeviations are computed using raw data on log(rit+ δ) and log(Sit/Ki,t−1); industry-adjustedstandard deviations remove industry (3-digit NAICS) fixed effects from both measures; andlong-run/industry-adjusted standard deviations remove industry fixed effects from firm-specificmeans of log(rit+δ) and log(Sit/Ki,t−1). In all cases, we assume the depreciation rate δ = 0.06.a The ratio of STD[log(rit + δ)] to STD[log(Sit/Ki,t−1)].

the second row accounts for heterogeneity at the industry (3-digit NAICS) level by first removing

industry means from both variables. By construction, these two measures allow for variation across

firms and time. To focus on long-run differences, the third row first computes the firm-specific

means of both measures and then computes the standard deviation of these long-run firm averages

relative to their industry means.

The results reported in the table indicate a much greater implied dispersion when the log of the

sales-to-capital ratio is used as a proxy for the user cost of capital, compared with the dispersion

based on observed interest rates. Depending on how one corrects for the inter-industry and within-

firm variation, we obtain dispersion measures based on measured marginal revenue products that are

about four times greater than those obtained using the cost of capital computed using observed firm-

specific interest rates. Focusing on the long-run measure, which likely captures the true average cost

of capital most accurately, these results imply that the Hsieh–Klenow methodology may significantly

overstate the TFP losses due to misallocation relative to the user-cost methodology in our data set,

provided that the misallocation mechanism is driven primarily by distortions in financial markets.

4.3 Time-Series Variation in Interest Rate Dispersion

A number of recent papers (Gilchrist, Sim, and Zakrajsek [2011], Khan and Thomas [2011], and

Arellano, Bai, and Kehoe [2012]) study the implications of increased dispersion in profitability on

resource allocation in macroeconomic models with various forms of financial market frictions. As

the severity of financial frictions increases, these models generally predict a greater dispersion of

financial outcomes across heterogeneous firms; for example, firms with low leverage and high cash

holdings can continue to borrow at relatively low cost, whereas those with high leverage and low

cash holdings can begin to face prohibitive borrowing costs during periods of financial turmoil.

To explore time variation in the dispersion of interest rates, the solid lines in Figure 6 show

the cross-sectional standard deviation of log(rit) over time and the quarterly growth rate of the

cyclically-adjusted total factor productivity as constructed by Basu, Fernald, and Kimball [2006].

23

Figure 6: Dispersion of Interest Rates and the Growth of TFP

-6

-4

-2

0

2

4

6

8

10

1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 20090.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8Percent StdDev(log r)

TFP growth (left axis)TFP growth trend (left axis)Interest rate dispersion (right axis)Interest rate dispersion trend (right axis)

Quarterly

Note: The dotted black line depicts the (annualized) quarterly growth rate of cyclically-adjusted TFP andthe solid black line depicts its corresponding H-P trend. The dotted red line depicts time path of the cross-sectional standard deviation of the logarithm of real interest rates for our sample of 496 manufacturing firmsand the solid red line depicts its corresponding H-P trend.

To abstract from fluctuations at business cycle frequencies, the dotted lines show the two series

deviated from the their respective local means using the Hodrick and Prescott [1997] (H-P) filter

with λ = 1, 600. According to the figure, the dispersion in real interest rates in U.S. manufacturing

was relatively low for the first decade or so of our sample period. In the late 1990s, however, the

dispersion of interest rates started to edge higher, increasing steadily through the 2001 economic

downturn and the aftermath of the bursting of the dot-com bubble. After leveling off in the mid-

2000s, interest rate dispersion again started to trend higher in 2007, increasing appreciably over

the remainder of the sample period.

As the dispersion in interest rates increased in the post-2000 period, the trend growth of TFP

also slowed notably. Although one cannot assign causality to these developments on the basis of a

simple correlation, this comovement is consistent with the notion that financial distortions reflecting

the past two finance-driven cyclical downturns have increased the misallocation of resources in the

economy and thereby reduced the pace of TFP growth. Given our calibration, the increase in the

trend dispersion of interest rates since the start of the 2007 recession can account for about 25 basis

points of the step-down in the annual TFP growth, assuming that financial frictions apply to both

labor and capital inputs. Clearly, this represents a non-trivial portion of the overall slowdown in

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trend TFP growth that has materialized during this time period.

5 Conclusion

This paper develops a tractable TFP accounting framework that is used to compute the resource

loss due the misallocation of inputs in the presence of financial market frictions. To a second-order

approximation, our methodology implies that resource losses may be inferred directly from the

dispersion in borrowing costs across firms. Using a direct measure of firm-specific borrowing costs,

we show that for a subset of U.S. manufacturing firms, the resource loss due to such misallocation

is relatively small—between 1.5 and 3.5 percent of measured TFP. On the whole, our results are

consistent with those of Midrigan and Xu [2010] and Hopenyahn [2011], who argue that financial

market frictions are unlikely to imply large efficiency losses in an economy with relatively efficient

capital markets.

It is important, however, to acknowledge several caveats to our methodology. First, to the extent

that firms experience direct credit rationing, the variation in observed interest rates understates

the true variation in the cost of capital. For our sample of publicly-traded manufacturing firms,

direct credit rationing seems rather implausible. Nonetheless, when measuring borrowing costs for

smaller firms in the U.S. economy or firms in developing countries, credit rationing may be of real

concern. Thus, while one might not directly observe the dispersion of interest rates that is ten

times greater than that observed in the U.S. financial data, credit rationing would certainly imply

greater dispersion in the shadow value of financial resources.

In addition, our accounting framework abstracts from the entry and exit of firms, along with

the potential selection effects that financial distortions may induce on those margins. In the United

States, however, incumbent firms account for the overwhelming share of economic activity, so such

selection effects are unlikely to be important—nevertheless, they may be of concern in developing

economies. Moreover, distortions in credit markets may influence the decision to employ one’s

human capital in an entrepreneurial capacity, a source of resource misallocation that can have sig-

nificant consequences for aggregate TFP, according to the recent work of Buera, Kaboski, and Shin

[2011].

Subject to these caveats, a clear advantage of our methodology is that it can easily be used to

study the question of what portion of the differences in TFP across countries may be attributable

to the misallocation of inputs arising from financial market frictions. Counterfactual experiments

indicate that a ten-fold increase in the dispersion in interest rates across firms implies a reduction—

through the effect of borrowing costs on resource allocation—in measured TFP of about 20 percent.

This finding implies that the dispersion in borrowing costs in developing countries must be an

order of magnitude greater than the dispersion of borrowing costs in the United States in order for

financial distortions to account for a significant share of the TFP differentials between developed

and developing economies.

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Moreover, it is well known that even in advanced economies such as the United States, there is

considerable dispersion in the observed marginal product of capital across production units. To the

extent that the dispersion in marginal products is not a result of measurement error, this implies

that the U.S. economy would realize significant productivity gains in response to optimal resource

allocation. However, the observed dispersion in the marginal product of capital in our data is four

times greater than the dispersion in the user cost of capital as measured by the firm-specific interest

rates. This divergences suggests that assigning all of the observed dispersion in factor input choices

to credit market distortions would substantially overstate the effect of financial frictions on resource

misallocation.

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